Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


David Bellhouse


In the setting of liver transplantation, clinical trials and transplant registries regularly collect repeated measurements of clinical biomarkers which may be strongly associated with a time-to-event such as graft failure or disease recurrence. Multiple time-to-event outcomes are routinely collected. However, joint models are rarely used. This thesis will describe important considerations for joint modelling in the setting of liver transplantation. We will focus on transplant registry data from the United States. We develop a new tool for joint modelling in the context where a critical health event can be tracked in the longitudinal biomarker and often presents as a non-linear trajectory with a sharp jump. We capture this non-linearity with a sin- gle change-point longitudinal component that is linked to the survival model via random effects in a way that incorporates the size of this change, which is a novel way to use a sharp change in the subject-specific random effect as a linkage in a joint model. We also propose an alternative to time dependent analysis of treatment effects by using a joint survival outcome model with a time-to-drug-failure event and a terminal event in graft failure that is more appropriate to use in drug effectiveness studies where subjects are discontinued from an immunosuppressant (in favour of alternative treatment) due to health reasons. Modelling drug regime failures as a time-to-event process has not been previously considered in transplant studies. We show that this method shows a significant association of time-to-drug-failure with time-to-graft-failure, whether applied with a longitudinal component or on its own in a joint survival outcome model.